Efficient routing schemes for multiple broadcasts in hypercubes

The authors analyze the problem in which each node of the binary hypercube independently generates packets according to a Poisson process with rate λ; each of the packets is to be broadcast to all other nodes. Assuming unit packet length and no other communications taking place, it is observed that the system can be stable in steady-state only if the load factor ρ≡λ (2^d-1)/d satisfies ρ<1 where d is the dimensionality (diameter) of the hypercube. Moreover, the authors establish some lower bounds for the steady-state average delay D per packet and devise and analyze two distributed routing schemes that are efficient in the sense that stability is maintained for all ρ<ρ* where ρ* does not depend on the dimensionality d of the network, while the average delay D per packet satisfies D⩽Kd(1+ρ) for small values of ρ (with constant K). The performance evaluation is rigorous for one scheme, while for the other the authors resort to approximations and simulations     

Comments on `Conditions for stable zeros of sampled systems' by M.Ishitobi

The commenter argues that the result of the above-titled work (see ibid., vol.37, no.10, p.1558-1561, Oct. 1992) is incorrect. It is pointed out that when sampling a continuous-time system G(s ) using zero-order hold, the zeros of the resulting discrete-time system H(z) become complicated functions of the sampling interval T. The system G(s) has unstable continuous-time zeros, s=0.1±i. The zeros of the corresponding sampled system start for small T from a double zero at z=1 as exp(T(0.1±i )), i.e., on the unstable side. For T>1.067 . . . the zeros become stable. The criterion function of the above-titled work, F(T)=G*(jω_s/2)= H(-1)T/2, is, however, positive for all T, indicating only stable zeros. The zero-locus crosses the unit circle at complex values     

Single-agent parallel window search

Parallel window search is applied to single-agent problems by having different processes simultaneously perform iteration of Iterative-Deepening-A* (IDA*) on the same problem but with different cost thresholds. This approach is limited by the time to perform the goal iteration. To overcome this disadvantage, the authors consider node ordering. They discuss how global node ordering by minimum h among nodes with equal f=g+h values can reduce the time complexity of serial IDA* by reducing the time to perform the iterations prior to the goal iteration. Finally, the two ideas of parallel window search and node ordering are combined to eliminate the weaknesses of each approach while retaining the strengths. The resulting approach, called simply parallel window search, can be used to find a near-optimal solution quickly, improve the solution until it is optimal, and then finally guarantee optimality, depending on the amount of time available     

Breaking substitution cyphers using stochastic automata

Let Λ be a finite plaintext alphabet and V be a cypher alphabet with the same cardinality as Λ. In all one-to-one substitution cyphers, there exists the property that each element in V maps onto exactly one element in Λ and vice versa. This mapping of V onto Λ is represented by a function T*, which maps any v∈V onto some λ∈Λ (i.e., T*(v)=λ). The problem of learning the mapping of T* (or its inverse (T *)^-1) by processing a sequence of cypher text is discussed. The fastest reported method to achieve this is a relaxation scheme that utilizes the statistical information contained in the unigrams and trigrams of the plaintext language. A new learning automaton solution to the problem called the cypher learning automaton (CLA) is given. The proposed scheme is fast, and the advantages of the scheme in terms of time and space requirements over the relaxation method have been listed. Simulation results comparing both cypher-breaking techniques are presented     

On quantization errors in computer vision

The author considers the error resulting in the computation of multivariable functions h(X₁, X, . . ., X_n), where all the X_is are only available in the quantized form. In image processing and computer vision problems, the variables are typically a mixture of the spatial coordinates and the intensity levels of objects in an image. A method is introduced using a first-order Taylor series expansion together with a periodic extension of the resulting expression and its Fourier series representation so that the moments and the probability distribution function of the error can be computed in closed form. This method only requires that the joint probability density function of X_i s be known and makes no assumption on the behavior on the quantization errors of the variables. Examples are also given where these results are applied     

Performance of shared memory in a parallel computer

A method for analyzing the lengths of memory queues when the network is conflict-free is described. An algorithm based on this method is shown to efficiently determine the upper and lower bounds of the queue length. Analysis indicates that the strategy of using hashing to spread data across memory modules is a good one. Results show that if the size of the system is increased while maintaining a constant ratio of numbers of processors to memories, then, asymptotically, the slowdown in performance from conflicts at the memory modules is Θ(log m /log log m). For m and n less than 100000 and λ between 0.25 and 4.0, the graphical data confirm this growth rate     

Linear stable unity-feedback system: necessary and sufficientconditions for stability under nonlinear plant perturbations

The authors consider a linear (not necessarily time-invariant) stable unity-feedback system, where the plant and the compensator have normalized right-coprime factorizations. They study two cases of nonlinear plant perturbations (additive and feedback), with four subcases resulting from: (1) allowing exogenous input to δP or not; (2) allowing the observation of the output of δP or not. The plant perturbation δP is not required to be stable. Using the factorization approach, the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps. Simple physical considerations explain the form of these necessary and sufficient conditions. Finally, the authors obtain the characterization of all perturbations δP for which the perturbed system remain stable     

Robust clustering with applications in computer vision

A clustering algorithm based on the minimum volume ellipsoid (MVE) robust estimator is proposed. The MVE estimator identifies the least volume region containing h percent of the data points. The clustering algorithm iteratively partitions the space into clusters without prior information about their number. At each iteration, the MVE estimator is applied several times with values of h decreasing from 0.5. A cluster is hypothesized for each ellipsoid. The shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the Kolmogorov-Smirnov test. The best fitting cluster is then removed from the space, and a new iteration starts. Constrained random sampling keeps the computation low. The clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm: multithresholding of gray level images, analysis of the Hough space, and range image segmentation     

An approach for pole assignment in singular systems

Pole assignment in a singular system Edx/dt=Ax+Bu is discussed. It is shown that the problem of assigning the roots of det(sE-(A +BF)) by applying a proportional feedback u=Fx+r in a given singular system is equivalent to the problem of pole assignment of an appropriate regular system. An immediate application of this result is that procedures and computational algorithms that were originally developed for assigning eigenvalues in regular systems become useful tools for pole assignment in singular systems. The approach provides a useful tool for the combined problem of eliminating impulsive behavior and stabilizing a singular system     

Observers for discrete singular systems

The author considers the design of observers for the discrete singular system Ex(k+1)=Ax(k)+Bu (k), y(k)=Cx(k), placing special emphasis on the problems of state reconstruction and minimal-time state reconstruction. It is shown that for a singular system, finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers     

Clustering on a hypercube multicomputer

Squared error clustering algorithms for single-instruction multiple-data (SIMD) hypercubes are presented. The algorithms are shown to be asymptotically faster than previously known algorithms and require less memory per processing element (PE). For a clustering problem with N patterns, M features per pattern, and K clusters, the algorithms complete in O(k+log NM ) steps on NM processor hypercubes. This is optimal up to a constant factor. These results are extended to the case in which NMK processors are available. Experimental results from a multiple-instruction, multiple-data (MIMD) medium-grain hypercube are also presented     

Some new results on optimal and suboptimal regulators of the LQproblem with output feedback

The LQ (linear quadratic) regulator problem with output feedback is considered. In the problem studies an output feedback control is determined such that the cost is J*, the optimal cost for the LQ problem with state feedback, or βj* with some constant β>1. A set of sufficient conditions is given for determining such optimal and suboptimal output feedback control laws     

Stability of x(t)=Ax(t)+Bx(t-τ)

A stability criterion for linear time-delay systems described by a differential difference equation of the form dx(t)=Ax(t)+Bx(t -τ) is proposed. The result obtained includes information on the size of the delay and therefore can be a delay-dependent stability condition. Its relation to existing delay-independent stability criteria is also discussed     

The stability of a family of polynomials can be deduced from afinite number 0(k3) of frequency checks

Let φ(s,a)=φ₀(s,a)+ a₁φ₁(s)+a₂ φ₂(s)+ . . .+a_kφ _k(s)=φ₀(s)-q(s, a) be a family of real polynomials in s, with coefficients that depend linearly on parameters a_i which are confined in a k-dimensional hypercube Ω_a . Let φ₀(s) be stable of degree n and the φ_i(s) polynomials (i⩾1) of degree less than n. A Nyquist argument shows that the family φ(s) is stable if and only if the complex number φ₀(jω) lies outside the set of complex points -q(jω,Ω_a) for every real ω. In a previous paper (Automat. Contr. Conf., Atlanta, GA, 1988) the authors have shown that -q(jω,Ω_a ), the so-called `-q locus', is a 2k convex parpolygon. The regularity of this figure simplifies the stability test. In the present paper they again exploit this shape and show that to test for stability only a finite number of frequency checks need to be done; this number is polynomial in k, 0(k³), and these critical frequencies correspond to the real nonnegative roots of some polynomials     

Efficient algorithms for system diagnosis with both processor andcomparator faults

For the comparison-based self-diagnosis of multiprocessor systems, an extended model that considers both processor and comparator faults is presented. It is shown that in this model the system diagnosability is t⩽Zδ/2Z, where δ is the minimum vertex degree of the system graph. However, if the number of faulty comparators is assumed not to exceed the number of faulty processors, the diagnosability of the model reaches t⩽δ. An optimal O(|E|) algorithm, where E is the set of comparators, is given for identifying all faulty processors and comparators, provided that the total number of faulty components does not exceed the system diagnosability, and an O(|E|)² algorithm for the case t⩽δ is also presented. These efficient algorithms determine the faulty processors by calculating each processor's weight, which is mainly defined by the number of adjacent relative tests stating `agreement'. After sorting the processors according to their weights, the algorithms determine all faulty components by separating the sorted processor list     

On the gap between the structural controllability of time-varyingand time-invariant systems

Structural controllability of time-invariant and time-varying systems when the input control sequences have a restricted length k is compared. The dimensions of controllable space coincide in the following three special cases: the input sequences have length k=2; the input sequences have k=n, where n is the size of the system (i.e., the ultimate controllability is the same in both cases); and for every length of input sequences provided that the system has a single input only. It is proved that there may appear a gap for every input length k such that 2< k⩽n/2. The case when n/2<k<n is left open     

Decoupling of square singular systems via proportional statefeedback

Necessary and sufficient conditions for the decoupling of a solvable square singular system Ex˙(t)=Ax(t)+Bu(t ) with output y(t)=Dx(t), through an admissible control law of the form u(t)=Kx(t)+Hr(t) where H is a square nonsingular matrix. It has been shown that for a given singular system that satisfies these conditions, a propagational state feedback exists for which the system's transfer function is a diagonal, nonsingular, and proper rational matrix. The proofs of the main results are constructive and provide a procedure for computing an appropriate proportional state feedback     

A parametrization of stabilizing controllers for multiratesampled-data systems

All linear multirate controllers for a given multirate sampled-data system plant are parameterized in terms of a single parameter Q(z) that is allowed to be any stable transfer matrix provided that certain causality conditions are met. The result parallels a well-known parameterization result for single-rate sampled-data plants. The parameterization suggests architectures for multirate controllers     

Constant time algorithms for the transitive closure and somerelated graph problems on processor arrays with reconfigurable bussystems

The transitive closure problem in O(1) time is solved by a new method that is far different from the conventional solution method. On processor arrays with reconfigurable bus systems, two O (1) time algorithms are proposed for computing the transitive closure of an undirected graph. One is designed on a three-dimensional n×n×n processor array with a reconfigurable bus system, and the other is designed on a two-dimensional n²×n² processor array with a reconfigurable bus system, where n is the number of vertices in the graph. Using the O(1) time transitive closure algorithms, many other graph problems are solved in O(1) time. These problems include recognizing bipartite graphs and finding connected components, articulation points, biconnected components, bridges, and minimum spanning trees in undirected graphs     

A unified task-based dependability model for hypercube computers

A unified analytical model for computing the task-based dependability (TDB) of hypercube architectures is presented. A hypercube is deemed operational as long as a task can be executed on the system. The technique can compute both reliability and availability for two types of task requirements-I-connected model and subcube model. The I-connected TBD assumes that a connected group of at least I working nodes is required for task execution. The subcube TBD needs at least an m-cube in an n-cube, m⩽ n, for task execution. The dependability is computed by multiplying the probability that x nodes (x⩾I or x⩾2^m) are working in an n-cube at time t by the conditional probability that the hypercube can satisfy any one of the two task requirements from x working nodes. Recursive models are proposed for the two types of task requirements to find the connection probability. The subcube requirement is extended to find multiple subcubes for analyzing multitask dependability. The analytical results are validated through extensive simulation